• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.741-751
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• 2022

The object of the present paper is to study some geometric properties of invariant submanifolds of N(k)-contact metric manifold admitting generalized Tanaka-Webster connection.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.525-535
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• 2019

In relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians and prove the non-existence of real hypersurfaces in $G_2({\mathbb{C}}^{m+2})$ with generalized Tanaka-Webster parallel structure Jacobi operator.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.57-68
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• 2015

In this paper, we give a non-existence theorem of Hopf hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, $m{\geq}3$, whose shape operator is of Codazzi type in generalized Tanaka-Webster connection $\hat{\nabla}^{(k)}$.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.881-896
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• 2019

In the present paper, we study certain curvature conditions satisfying by the projective curvature tensor in Sasakian manifolds with respect to the generalized-Tanaka-Webster connection. Finally, we give an example of a 3-dimensional Sasakian manifold with respect to the generalized-Tanaka-Webster connection.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.473-486
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• 2021

We prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the k-th generalized Tanaka-Webster connection.